Automatic code generation for high-performance Discontinuous Galerkin methods on modern architectures
SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software’s sustainability. In this publication, we solve this sustainability and performance portability issue by enriching the simulation...
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| Main Authors: | , , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
December 2020
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| In: |
ACM transactions on mathematical software
Year: 2020, Volume: 47, Issue: 1, Pages: 1-31 |
| ISSN: | 1557-7295 |
| DOI: | 10.1145/3424144 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1145/3424144
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| Author Notes: | Dominic Kempf, René Heß, Steffen Müthing, and Peter Bastian |
MARC
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| 245 | 1 | 0 | |a Automatic code generation for high-performance Discontinuous Galerkin methods on modern architectures |c Dominic Kempf, René Heß, Steffen Müthing, and Peter Bastian |
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| 520 | |a SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software’s sustainability. In this publication, we solve this sustainability and performance portability issue by enriching the simulation framework dune-pdelab with a code generation approach. The approach is based on the well-known domain-specific language UFL but combines it with loopy, a more powerful intermediate representation for the computational kernel. Given this flexible tool, we present and implement a new class of vectorization strategies for the assembly of Discontinuous Galerkin methods on hexahedral meshes exploiting the finite element’s tensor product structure. The performance-optimal variant from this class is chosen by the code generator through an auto-tuning approach. The implementation is done within the open source PDE software framework Dune and the discretization module dune-pdelab. The strength of the proposed approach is illustrated with performance measurements for DG schemes for a scalar diffusion reaction equation and the Stokes equation. In our measurements, we utilize both the AVX2 and the AVX512 instruction set, achieving 30% to 40% of the machine’s theoretical peak performance for one matrix-free application of the operator. | ||
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